The wide arched opening as it related to the ceiling change and the wing-wall to the left of the refrigerator looks odd. I have never thought a corner pantry looks good or functions well.

Can you show the floor plan of the kitchen and all the spaces that surround it?

Sure. Here you go. Here's the floor plan and also a photo I found online of the kitchen. There was supposed to be a cased opening between the living room and kitchen, but I chose to do the arch. I had made that decision before finding out that the kitchen ceiling would need to be lowered. I'm really stressing on what I should do now to make this plan look better.

Should I insist on the dining room ceiling being lowered to 9 ft as well?

Get rid of the arch.

And do you still have a chance to change your kitchen layout?

Unfortunately, no. I wish I could, but the cabinets have already been paid for and ordered. If I had a do-over, I would have moved the refrigerator over to the wall on the right. Then we wouldn't need that wing wall.

If I got rid of the arch, what do you suggest? Should I just leave it open to the living room? I'm afraid it would still look odd with the kitchen being 9 ft and the dining room being 10 ft.

The image looks like a bad remodeling where someone bought an older home with a room for a living room, a room for a dining room and a room for a kitchen, and opened up the walls between the rooms as much as they could with total disregard for definition of space. As if they wanted open concept, but fell short. At your point of construction, there is not much that can be done.

There is a lot with the floor plan I would do differently..

Yes to Mark’s additional walls between the kitchen, the living room, and the dining room. I am confused about why the passage way from the kitchen to the living room is an arch, the doorway to the mud room is arched, yet the area from the kitchen to the dining room is a squared off entrance. You need to craft an arch between the kitchen and dining room by creating the little wall “L” at the corner. And shorten the arch between the kitchen and living room. These arches will then frame the transition between these three rooms, mask the lower ceiling in the kitchen and echo the other arches that are elsewhere in your house.

I would square out all the arches. Unless you have an old Spanish style house, most people are removing the arches when remodeling their 1990s faux mediterranean/spanish style houses. In my area people are also removing any arched windows when remodeling and going with simpler cleaner lines.

I think a 9' ceiling in a kitchen is great it allows for cabinets to the ceiling and honestly i see no reason to have a 10' ceiling at all. Too bad you did not come here before the kitchen design was done by a cabinet sales person I bet .Waht exactly is the reason for the arches? IMO you do all arches or no arches .An architect and an actual KD would have been good ideas from the start. IMO the wall creates the separation between the 2 space so no big deal . Things like fake beams are never IMO a good choice and for sure not added to this mix of confusion